MACHINE 
DRAWING 



L A. WIRICK. 



MACHINE D RAWING 



FOR USE OF STUDENTS IN 

INDUSTRIAL AND CONTINUATION 

SCHOOLS 



BY L. A. WIRICK 



^The lessons outlined in the following pages are elementary in 
character, being intended for beginners in the subject. They are 
more particularly applicable to the making of working drawings as 
used in the manufacture of machinery, and are to some extent in- 
troductory to machine design. The principles of mechanical draw- 
ing, however, apply to all branches of the subject. 



PRINTED BY BELOIT EVENING SCHOOL 

BELOIT, WISCONSIN. 






Copyiighi 1914, by L. A. WIRICK. 



o.r 



©CI.A376904 

^% -5 19/4 



CONTENTS. 



PART I. The Making of Lines. 

Sections 1 to 10. Materials and instruments used 
in making drawings; the use of tee square, tri- 
angles, compasses, dividers and scale; making 
straight lines, circles, parallels and perpendic- 
ulars; scale drawing; construction lines; lettering. 

PART II. The Meaning of Lines. 

Sections 11 to 16. Surfaces, edges and limits; 
views, invisible parts, sections; arrangement of 
views; reduced and enlarged scales. 

PART III. Working Drawings. 

Sections 17 to 20. Construction of drawings 
from notes and sketches; sketching from ma- 
chine parts; conventions, stock parts, use of 
reference tables. 

PART IV. Tracings and Blue prints. 

Sections 21 to 23. Materials for tracing, order 
of tracing; shade lines; blue prints. 

PART V. Projections. 

Sections 24 to 28. Definitions, orthographic pro- 
jection, third angle; auxihary views; inter- 
sections. 



nnHE PLAN of this book comprises, first, instruc- 
*■ tion in the theories upon which working draw- 
ings are based; second, directions as to the manner 
in which these theories are to be applied in the making 
of working drawings; third, exercises illustrating 
their application. The book should be carefully stud- 
ied as a text book and be kept at hand for reference. 
The exercises are numbered and printed on separate 
pages, (Job sheets) following the sections explaining 
them. Each job should be worked out when its num- 
ber is reached, indicated by 5-a etc., before passing 
to the next paragraph. In the exercises of Part I the 
instruments needed for each exercise are mentioned, 
and no others should be used. The exercises given 
form a minimum amount of work in connection with 
the various topics. 



CORRECTIONS. 
Page 9. Sec. 6. at end add 6-c 
Page 23. 12-c shonld read I3-c. 
Page 28. after 17-c. read 1 7-d instead of I 7-b. 
Page 36, 21 -a should read 21-d. 



MACHINE DRAWING 

PARTI. - - - - THE MAKING OF LINES 



Mechanical drawing is so called because in- 1 
struments are used in making the drawings. The 
principal uses of such drawings are in connection with 
the manufacture of machinery and in the practice of 
architecture and civil engineering. The general prin- 
ciples of drawing are the same in all branches. The 
details of the operation depend upon the purposes for 
which the drawings are made. 

A working drawing is for the use of the persons 
making the thing represented and should comprise all 
the information needed by them, so that the finished 
object will be exactly what was intended by the de- 
signer. To accomplish this the drawing must be ac- 
curate, complete and clear. Drawings are usually 
made on common drawing paper in pencil and then 
copied in ink by tracing them on transparent paper 
or cloth. The tracings are then used in making blue 
prints which are sent to the shops as needed. 

Drawing paper is made in a variety of 2. 
grades, of several colors, either in sheets of 
standard dimensions or in continuous rolls. For ordi- 
nary drafting room purposes buff roll paper 36 inches 
wide is supplied. This is cut into sheets as needed a 
usual size being 18 in. by 26 in. The drawing itself is 
made to occupy an inch or two less than these di- 
mensions. Tracing cloth is also in rolls and is cut 
to the same size sheets for use. When the tracing 
is finished it is trimmed to a standard size, say 17 in. 
by 24 in., which is a convenient size for filing and 
makes prints of a size suitable for shop use. 



The drawinji- paper and tracing cloth are used on 
a smooth table or drawing board to which they are 
fastened with thumb tacks. The left hand end of the 
table or board must be perfectly straight for the tee 
square. 

The number and character of the instruments 
depends somewhat upon the character of the work to 
be done. Nine-tenths of the ordinary work done in a 
drafting room can be done with a very simple set of 
instruments. The following may be considered es- 
sential. 

Tee square, Compasses, Bow pencil. 

Two triangles, Dividers, Bow pen. 

Scale, Ruling pen. 

To these must be added a drawing board and a 
supply of pencils, erasers, pens, drawing ink, drawing 
paper, tracing cloth, thumb tacks, and a sand paper 
block. In addition to the list given, which may be con- 
sidered a standard outfit, there are a few other 
instruments of value in particular cases. The fol- 
lowing are suggested as being of frequent service. 
Extra scales. Protractor, Wide ruling pen. 
Extra triangles. Curve, Erasing shield. 

It is advised that greater expenditure should be 
in the way of better quality, rather than a greater 
number of instruments. 

The manner of using the instruments will be ex- 
plained in connection with the exercises calling for 
their use. 

3. The purpose of a working drawing is to con- 
vey information from the designer of a machine 
to the persons who make the machine and its parts. 
Before a thing can be made it is necessary to know 
its shape and size. A working drawing gives this in- 
formation by means of lines of various kinds and let- 
ters and figures so related to ea*h other as to be under- 



stood by the various workmen. A working drawing 
is not a picture, but differs in many respects from the 
artist's production. Its sole purpose is to convey in- 
formation; to present the object as it is, rather than as 
it may appear to be. 

The lines of a drawing are principally 4. 
straight lines and circles or parts of circles. 
In a pencil drawing, certain lines used only for con- 
struction purposes are made very light. The regular 
lines of the drawing should be firm and distinct and 
may be either full or broken. Ink Bnes (as used in 
tracing) should be made of several widths according 
to their meaning. 

The pencil for drawing lines should be rather 
hard, 5H or 6H, and should be sharpened to a smooth 
flat end. A piece of fine sand paper or emery cloth 
glued on a block of wood is needed for keeping the 
point in good order. 

Straight lines are made by use of a straight- 5. 
edge, such as the edge of the tee square or tri- 
angle. Only the upper edge of the tee square or the 
further edge of the triangle should be used as the 
ruUng edge. Horizontal lines and inclined lines are 
drawn from left to right. Vertical lines and inclined 
lines approaching the vertical are drawn upward ex- 
cept when near the right hand end of the drawing 
board, where a downward stroke is more convenient. 
The pencil should be held with the flat side of the 
lead against the straightedge, with the point a little 
away from the edge so as to show daylight between 
the edge and the line when drawn. 5-a. 5-b. 

Horizontal lines are drawn by using the tee 
square, the head of which is held against the left 
hand end of the drawing board. Note that all hor- 
izontal lines are parallel. 5-c. 5-d. 
7 



Vertical lines are drawn by using a triangle with 
the tee square. Place one leg of the triangle against 
the tee square and use the other leg as the ruling 
edge. Note that all vertical lines are parallel to each 
other, and that horizontal and vertical lines are per- 
pendicular to each other. 5-e. 5-f. 

Oblique lines are drawn by using one or both tri- 
angles with the tee square, or by using a single 
straight edge. The triangles in common use have 
angles of 30° and 60° on one and of 45° on the other. 
When used singly with ths tea square, these will give 
lines inclined in six directions. By placing one triangle 
against the tee square and the other against the first, 
it is possible to get lines inclined in four more direct- 
ions. It is more convenient to use the triangles in this 
way than to resort to the use of a protractor when the 
required angle is a multiple of IS"*. 5-g. 5-h. 

A line can be drawn through two points by plac- 
ing a straight edge to them. The edge should not 
coincide with the points but should leave equal day- 
light between them and the edge. A point is usually 
located by the intersection of two lines or by a light 
indentation by the point of the dividers. 5-k. 

A line can be drawn parallel to a given line as 
follows. Place a triangle so that one side coincides 
with the given line and place the tee square against 
one of its other sides. Slide the triangle along the tee 
square and its edge will always be parallel to the 
given line. 5-m. 

A line can be drawn perpendicular to a given line 
as follows. Place a triangle so that its hypothenuse 
coincides with the given line and place the tee square 
against one leg of the triangle. Hold the tee square 
in place and reverse the triangle so that its other leg 
is against the tee square. The hypothenuse is now^ 



perpendicular to the given line and can be moved along 
the tee square to any desired position. 5-n. 5-p. 

Circles are drawn with compasses fitted with 6. 
pencil or ruling pen. For small circles a bow pen- 
cil or bow pen is used, for large ones a beam compass. 
The center of a circle is indicated by the intersection 
of two center lines, usually horizontal and vertical. 
Center lines are light lines made up of alternate long 
and short dashes. They do not represent an actual 
part of the object shown in the drawing but are con- 
struction lines used for convenience in constructing 
the drawing and in making the object itself. After 
adjusting the compasses to the required dimension 
(radius) it is manipulated by its handle with one hand. 
It should be swung around clockwise, with its top 
slightly inclined forward. 6-a. 6-b. 

Tangent lines are of frequent occurrence in 7. 
machine drawing, either a straight line and a 
circle meeting, or two arcs making a compound curve. 
A circle and a tangent to it coincide at one point and 
a radius at this point is perpendicular to the tangent. 
Two circles or arcs tangent to each Other coincide at 
one point and this point is on a straight line passing 
through the two centers. The point where two tan- 
gent lines meet or coincide has a definite location, 
but if the lines are properly drawn the point cannot 
be determined by inspection. Its location can be ac- 
curately determined by a simple construction based 
on the geometrical facts just stated. This rule works 
both ways and is useful for drawing a tangent arc 
from a given point on a straight line or circle and 
for drawing a straight line tangent to a circle at a 
given point. 7-a. 7-b. 7-c. 7-d. 



8. Dividers are used for dividing a line into a 
given numb-r of parts, or for setting off a line 

equal to a given line or dimension. The dividers 
should not be used for taking dimensions from the 
scale when the scale can as well be applied directly 
to the drawing. It is pro.ier to use the dividers f:r 
this purpose when the same dimension is to be used 
in several places or repeated along a line. Do not 
set the points of the dividers or of any other instru- 
ment on the scale itself, but on the paper or board 
along the edge of the scale. 8-a. 8-b. 

9. An important purpose of a working drawing 
is to show the size of the piece to be made. The 

lines of a drawing represent corresponding lines of 
the object, and when the lines of the drawing are 
proportional in length to the lines of the object the 
drawing is to scale. Working drawings should al- 
ways be made to scale. If the lines of the drawing 
are of the same actual length as the corresponding 
lines of the object, the drawing is full size or full 
scale. In any drawing made to scale, whether full 
scale or otherwise, the size of the object can be de- 
termined by measuring the lines of the drawing. 
This is the usual method in some kinds of architect- 
ural drawing, but on engineering drawings the sizes 
are given by figures and dimension lines and the 
drawing should not be measured. The arrange- 
ment of dimension lines and witness or reference 
lines is shown in Chart I. 

The dimensions which should be given on a draw- 
ing are those which will be needed by the persons 
using the drawing, and they should be given in such 
a way that the pattern maker, lay-out man, machin- 
ist or other mechanic can get the dimension he re- 
(luires directly from the drawing. 



The first rule is to work from center lines if there 
are any; second, give dimensions from finished edges 
rather than from unfinished ones; third, given di- 
mensions where fits and clearances are required. 
The location of the dimension fines should be such as 
ot interfere as fittle as possible with the drawing it- 
self. Figures should read from the bottom and right 
hand end of the sheet and in the run of the dimen- 
sion line. For circles give the diameter rather than 



TH/SS/ZE/i/iD STYLE OF LETTERS /S 
SU/TABLE FOR GENER/iL USE or/ [A/ORK- 
JNG DRAW/nOS. HE/eHT /sfzT SLANT 
ABOUT 25 ". F/SL/RES /234-5e 7&90. 

THIS SIZE FOR Tl TLBS. 



V/S/BL£ OUTLtNE 



/fiV/S/BLE. SECTfON RL/^NE. 



CE/VTER L/riE. 



M^" 



The Alphabet of Lines and Let;ers. 

the radius; for an arc give the radius. Do not re- 
peat a dimension on another view. Do not put fig- 
ures on a line used for any other purpose than as a 
dimension line. 

The scale used for laying off dimensions should 
be of a character suited to the work being done. 
Architectural work is all laid out in feet and inches; 



hence the architect's scale has the units, represen- 
ting feet, divided into twelfths, representing inches. 
Civil engineering work is fre(iuently laid out in feet 
and tenths; hence the engineer's scale shows decimal 
divisions. Machine work is almost entirely laid out 
in inches and binary fractions; hence on the scale 
best suited to this kind of drawing, the units are di- 
vided into halves, quarters and eighths. 

In using a scale it should be applied to the draw- 
ing and the dimensions marked off as required. 9-a. 
9-b. 9-c. 

10. Besides the lines of the drawing itself and the 
construction lines used with them, a drawing 
contains figures forgiving the dimensions and letters 
for notes sometimes required to make the drawing 
entirely clear. The most important thing in regard 
to letters and figures is that they must be distinct. 
A style and size in common use is shown in Chart I. 
Lettering is done freehand with a finger stroke, 
avoiding almost entirely upward or backward move- 
ments. Use a round pointed medium pencil (about 
4H). Draw guide lines for the top and bottom of 
each line of words. Care must be used in spacing 
between lines, between words and between the letters 
in a word. Uniformity of height and slant will add 
greatly to the legibility and neatness. 



^ Never use the scale as a straightedge for draw- 
ing lines. 

^ Never use the tee square against any side of the 
drawing board except the left hand end. 

Q Never use a carpenter's or machinist's scale for 
drafting purposes. 



MACHINE DRAWING-Job Sheet No. 1 



5-a. (Straightedge.) Draw several straight lines about 
3 in. long, in different directions. Do not measure. Make 
the ends distinct and definite. 

5-b. (Straightedge.) Draw two intersecting lines and 
through the point of intersection draw several more lines. 
Care must be used that all the lines pass exactly through 
the one point. 

5-c. (Tee square.) Draw several horizontal lines side 
by side, about 3 in. long and 1-4 in. apart. Do not 
measure. 

5-d. (Tee square.) Refer to 5-a. Select one of these 
lines and from each end of it draw a horizontal line to 
the right. Select another line and draw two horizontal 
lines ending at the given line without crossing it. 

5-e. (Tee square and triangle.) Draw several vertical 
lines side by side, about 3 in, long and 1-4 in. apart. Do 
not measure. 

5-f. (Tee square and triangle.) Refer to 5-c. Draw 
several vertical lines across these lines but not extending 
beyond the top and bottom lines. 



MACHINE DRAWING-Job Sheet No. 2 



5-g. (Tee square and 45° triangle.) Draw horizontal 
and vertical intersecting lines and through the intersec- 
tion draw two 45° lines. 

5-h. (Tee square and two triangles.) Draw horizontal 
and vertical intersecting lines and through the intersec- 
tion draw lines inclined at all 15° intervals. Note that 
this makes a symmetrical figure, dividing the space 
around the point into 24 equal angles. 

5-k. (Triangle.) Draw three pairs of intersecting lines 
thus locating three points. Connect the three points with 
three straight lines, making a triangle. 

5-m. (Two triangles.) Refer to 5-a. Draw a line par- 
allel to each of these lines and about 1-4 in. distant. 

5-n. (Two triangles.) Refer to 5-b. Determine if any 
of these lines are perpendicular to each other. 

5-p. (Two triangles.) Refer to 5-k. Through each apex 
of this triangle draw a line perpendicular to the oppo- 
site side of the triangle. Note whether these three lines 
intersect in one point. 



MACHINE DRAWING-Job Sheet No. 3 



6-a. (Tee square, triangle and compasses.) Draw a cir- 
cle about 2 in. diameter. Locate the center by means of 
horizontal and vertical center lines before drawing the 
circle. On the same center draw another circle a little 
larger than the first one and another a little smaller. 

6-b. (Tee square, triangle bow pencil and compasses.) 
Set the 'bow pencil at about 3-4 in. and draw two equal 
circles tangent to each other and having their centers on 
the same horizontal center line. Draw another circle that 
will exactly enclose (circumscribe) the other two. Note 
the location of the center of the large circle. 

6-c. (Tee square, 30-60 triangle, compasses and bow 
pencil.) Draw 6 circles 1-2 in. diameter equally spaced 
on a 4 in. circle. There should be horizontal and vertical 
center lines for the 4 in. circle. The 4 in. circle should 
be considered a center line for the small circles. The 
other center line for each small circle should be a short 
radial line. 



MACHINE DRAWING-Job Sheet No. 4 



7-a. (Tee square, triangle and compasses.) Draw an 
arc about 2 in. long with a radius of about 2 in. From 
each end of the arc draw a tangent line about 2 in. long. 

7-b. (Tee square, triangle and compasses.) Draw a 
straight line about 3 in. long. At each end draw a tan- 
gent arc of 90° (exact) with a radius of about 1 1-2 in. 

7-c. (Tee square, triangle and compasses.) Draw a cir- 
cle about 2 in. diameter. Draw two horizontal and two 
vertical lines touching the circle (tangents). Draw a 
circle passing through the intersections of the four 
straight lines. 

7-d. -(Tee square, 30-60 triangle and compasses.) Draw 
a vertical line and two lines inclined 60° from it all 
passing through one point. With this point as a center 
draw a circle about 2 in. diameter. At each point where 
the circle intersects a straight line, draw a line tangent 
to the circle, making a hexagon. 



MACHINE DRAWING-Job Sheet No. 5 



8-a. (Tee square, dividers and triangle.) Draw two 
horizontal lines about 2 in. long and 1-2 in. apart, side 
by side. Draw two vertical lines exactly the same length 
and the same distance apart, crossing the two horizontal 
lines so as to make a symmetrical figure. A symmetrical 
figure should have center lines showing the axes of sym- 
metry. 

8-b. (Tee square, triangle, compasses and dividers.) 
Draw a circle about 3 in. diameter. Divide the circum- 
ference into 5 equal parts and draw a radius to each 
point. 

9-a. (Triangle and scale.) Refer to 6-c. Draw a line 
diagonally across the large circle, measure this diameter 
and put down the figures on the dimension line. 

9-b. (Tee square, triangle and scale.) Refer to 7-d. 
Draw horizontal witness lines in extension of the top 
and bottom sides of the hexagon, draw a dimension line 
between them, measure the distance and put in the 
dimension. ; 



MACHINE DRAWING-Job Sheet No. 6 



9-c. (Tee square, 45° triangle and scale.) Make a draw- 
ing as shown in Fig. 5, the dimensions being 3 in. by 
4 1-2 in. for the outer rectangle, with 1-2 in. space be- 
tween it and the inner rectangle. Note that the 
drawing consists of 4 horizontal lines and 4 vertical 
lines, spaced so as to give the required size. First 
lay the scale on the pa- 
per along the tee square 
and mark off 4 points 
locating the four ver- 
tical lines. Shift the 
scale and mark off 4 
points for the horizont- 
al lines. These "points" 
are light pencil lines 
Fig. 5. Job No. 9-c. about 1-32 in. long. 

Draw 4 light (construction) lines with the tee square 
thfough the last 4 points about 5 in. long. Draw the 4 
(heavy) vertical lines through the first 4 points and 
terminating at the construction lines. Draw the 4 
(heavy) horizontal lines coinciding with the construc- 
tion lines but ending exactly at the ends of the 4 ver- 
tical lines. Draw the 45? lines spaced 3-32 in. apart, 
beginning at the upper left hand corner. Do not meas- 
ure this spacing but get it uniform. 




MACHINE DRAWING 

PART II. - - - THE MEANING OF LINES 



The lines of which a drawing is composed 1 1 . 
are arranged to represent the corresponding 
lines of the object drawn. 

The surfaces of an object may be of any number 
and are either plane or curved. Where two surfaces 
meet there is an edge, more or less acute, and this 
edge is represented by a line of the drawing. 

If a curved surface of an object is only partly 
visible, there is an imaginary line separating the vis- 
ible from the invisible part. This line is also repre- 
sented by a line of the drawing. 

Hence the lines of a drawing represent two dif- 
ferent things: the edges of the different surfaces of 
the object, and the boundary lines of the visible parts 
of car\^ed surfaces. Usually no distinction is made 
between these two meanings. 

From any particular point of view, one or 12. 
more of the surfaces of an object may be seen, 
but not all of them. Consequently, one view in a 
drawing is not sufficient to give complete information 
as to all parts of the object. By looking at it from 
different directions, enough views may be made to 
show all parts of the object and thus furnish complete 
information. The point of view may be in any direc- 
tion from the object. For working drawings the po- 
sitions usually taken are directly above or below, in 
front of, or at either side, giving top, bottom, front 
and side or end views. These may be considered the 
six standard views. The view from directly above is 
a plan and that from any side is an elevation. 



Consider a cube. It has six surfaces, or faces. 
As seen from above or below or from any side, it pre- 
sents one face only, which is a square figure, and the 
drawing of each view is composed of four straight 
lines representing the four edges of the one visible 
surface. 

Consider a cylinder. It has three surfaces, two 
plane and one curved. A view of either end presents 
one surface, the drawing of which is a circle repre- 
senting the edge. As seen from any side, it presents 
one half of the curved surface. A drawing of any 
side consists of four straight lines, two of which rep- 
resent the edges where the curved surface joins the 
ends, and the other two represent the limits of the 
visible part of the curved surface. 

Consider a sphere. It has but one surface, uni- 
formly curved. As seen from any direction it pre- 
sents one half of this curved surface. The drawing 
of any view of a sphere is a circle, representing the 
boundary line of the visible half of the surface. 

These geometrical bodies are typical of the forms 
occuring in machine parts. Any object may be con- 
sidered in the same way making a study of the dif- 
ferent surfaces and edges. Drawings of the differ- 
ent views will be made up of lines representing the 
edges if there are any, and the furthest visible 
points or lines of the curved surfaces. 12-a. 

It is seldom necessary to draw all of the six stand- 
ard views of an object. In a majority of cases two 
or three are sufficient. Additional views should be 
made whenever greater clearness can be obtained by 
so doing. On the other hand, additional views which 
give no additional information should not be made. 
The draftsman must decide from the circumstances 
of each particular case how many views and what ones 
will give the best results. 



Parts of an object which are not visible from 1 3. 
a given point, may, nevertheless, be shown in 
the view from that point. Such parts are shown by 
broken lines made up of short dashes. The arrange- 
ment of these lines is the same as though the invis- 
ible part were seen through the part that hides it 
from view. Hollow parts, or holes into or through an 
object are shown in the same way as other invisible 
parts. 13-a. 13-b. 13-c. 

The arrangement of the different views of 14. 
an object in relation to each other follows def- 
inite rules of projection. These rules and principles 
will be more fully explained in Part V. A working ex- 
planation sufficient for practical purposes is given 
here. Of the six standard views, one may be consider- 
ed the principal view and the others are arranged 
with reference to it. The principal view should be the 
one showing the most detail or the most characteris- 
tic features of the object. It is desirable, but not essen- 
tial, that this view should show the object " right side 
up" or in its normal position in the completed machine. 
Let this be considered a front view. A right end view 
is drawn at the right hand of the front view, a left end 
view at the left hand. A top view, or plan, is drawn 
above the front view. A bottom view is drawn below 
the front view. 

The six standard views of an object can be ar- 
ranged in a model which will clearly demonstrate the 
required arrangement. Make the six views each on 
a sheet by itself. Draw a border line one inch out- 
side of the drawing and trim each sheet to this line, 
making a rectangular card. Arrange the six cards 
in the form of a box, the drawings on the outside, and 
fasten them together with strips of gummed paper. 
Care must be used to have the drawings correspond 



in position to the parts of the object they represent. 
Now cut enough of the gummed strips to allow the 
six cards to be spread out flat, but remain attached 
to each other. The drawings thus shown have the 
correct relation to each other. It is evident that sev- 
eral different arrangements may be obtained by cut- 
ting the strips in different places, all of which are cor- 
rect. 14-a. 

15. A section or sectional view is a convenient 
means of showing the shape of an object at any 

particular transversal. It is made by assuming that 
a part of the object is cut away so that a certain in- 
visible part becomes visible. The part of the object 
remaining beyond the plane of the section, or cutting, 
is drawn in the regular way, although frequently 
only the cut surface is shov/n, the parts beyond be- 
ing omitted. To show that the view is a section, 
the part representing the cut surface is hatched by 
oblique parallel li:i23 which should be light and uni- 
form. A note is also added to show the location of 
the section, referring to a similar note on some other 
view. 15-a. 15-b. 

16. It is not always possible or desirable to make 
a drawing full scale. Some pieces are too large 

to be conveniently drawn in this scale, or so much 
lacking in detail that a full scale drawing is not as 
clear as a smaller one. Other pieces are so small that 
a full scale drawing would be illegible. For these 
reasons various other scales are used to secure the 
necessary size ..nd clearness. The usual scales for 
working drawings, besides full size, are half size, 
quarter size and eighth size, frequently called 6 in., 
3 in. and 1 1-2 in. to the foot, respectively. For small 
objects, double size scale may be used. 



To use any selected scale, consider each unit on 
the scale to represent an inch, and lay off the required 
dimensions in the regular way. Do not form the habit 
of thinking of the dimensions on a reduced scale 
drawing as the full dimensions divided by two, four, 
etc., but a3 ths full number of units. The figures to 
be used in giviag the dimensions are such as to indi- 
cate the full size of the object regardless of the size 
of the drawirg. 



^ For preliminary practice in using other than full 
scale, make an arbitrary scale by setting the dividers 
at random,— about the length of the ruled dash above 
this paragraph— and set off this dimension a number 
of times along the edge of a strip of drawing paper. 
Number these points in order and divide each space 
into halves, quarters and eighths. Use this scale for 
making a drawing of a piece such as 12-c. 

^ To avoid the necessity of dividing the diameter 
by two for the radius, set the compasses to the given 
dimension on a scale half the scale being used. 

The scheme is also useful for laying off half of a 
given dimension on each side of a line. 

^ It is sometimes thought to be advantageous to use 
different styles of cross-section hatching to indicate 
different materials. Several systems of such conven- 
systems of such conventional hatching lines have been 
devised, but a complete system is manifestly impos- 
sible. In the absence of general agreement and un- 
derstanding, a key to an .- system in use is required. 
The scheme is of questionable value and should not be 
employed on working drawings unless required by the 
rule=! or custom of the place. 



Decimal Equivalents. 



■5 DECIMAL 



^'Si^S °°S?3JS 









I 


.015625 


" 






33" 


.515625 






1 


3 


.03125 
.046875 






17 


35 


.53125 
.546875 




1 


3 


- 
5 

7 


.0625 
.078125 
.09375 
.109375 




9 


19 


37 
39 


.5625 
,578125 
.59375 
.609375 


1 


- 


- 


9 


.125 

.140625 


5 






41 


.625 
.640625 






5 


11 


.15625 
.171875 






21 


43 


.65625 
.671875 




3 


7 


13 
15 


.1875 
.203125 
.21875 
.234375 




11 


23 


45 
47 


.6875 
.703125 
.71875 
.734375 


2 


5 


9 


17 
19 
21 


.25 

.265625 

.28125 

.293875 

.3125 

.328125 


6 


13 


25 


49 
51 
53 


.75 

.765625 

.78125 

.796875 

.8135 

.828125 






11 


23 


.34375 
.359375 






27 


55 


.84375 
.859375 


3 


.- 


- 


25 


.375 
.390625 


7 


- 




57 


.875 
.890625 






1 


27 


.40625 
.421875 






29 


59 


.90625 
.921875 




"7 




29 
31 


.4375 
.453125 
.46875 
.484325 




15 


31 


61 
63 


.9375 
.953125 
.96875 
.984385 


4 


- 






.5 


8_ 


_:_ 


__.!_ 


- 


1.000 



Arithmetical Constants. 

Ratio of Circumference to Diameter, Fi, - 3.1416. 
Reciprocal of Pi, - - . • - .3183. 



24 



MACHINE DRAWING-Job Sheet No. 7 



i2-a. Draw 6 views of a piece of bar steel 1 in, by 1 1-4 
in. by 4 1-2 in. long which has been turned to 1 in. 
diameter for a length of 2 in, from one »nd, 

13-a. Draw a top view of a piece of cast iron 4 in, square 
in the bottom of which is a round hole 2 in. diameter, 

13-b. Draw a top view of a piece of cast iron 4 in. square 
on the bottom of which is a round boss 2 in, diameter, 

13-C Draw two views of a bar 1 3-8 in, square by 4 in, 
long with a 3-4 in. hole drilled through it lengthwise. 

14-a. Refer to 12-a, Select two of these six views 
which will be sufficient to give complete information 
and redraw them in proper relation to each other, 

15-a. Refer to 13-a, Draw a section of this piece show- 
ing a thickness of 2 in,, and the round hole 1 1-4 in, deep, 

15-b. Draw a top view (face view) and a center-line 
section of an 0-G cast iron washer 2 1-8 in. to 2 7-8 in. 
diameter by 3-4 in. thick, with a hole 1 1-16 in. diameter. 



MACHINE DRAWING 

PART III. - - - WORKING DRAWINGS 

Drawings may be constructed from a mental 1 7. 
conception of the object to be made; from notes 
describing the object; from a sketch of the object; 
from a drawing already in existence, or from the 
object itself. The draftsman must indeed always have 
a mental conception of the object he is drawing, but 
this may be derived from any of the sources enume- 
rated. The designer of a machine may put his ideas 
into a drawing or he may record them in notes and 
sketches to be worked out by a draftsman. The notes 
can also be translated into sketches and these in turn 
accurately redrawn. If the drawing is to represent 
an object already in existence a sketch is a conven- 
ient means of recording the necessary data as obtain- 
ed by inspection and measurement of the object. 

A sketch differs from a drawing in being made 
free hand, and is not always complete, especially 
when used only as a memorandum. When it is to be 
the basis of a working drawing it should be as com- 
plete as the drawing itself. This is particularly the 
case where it is used as an intermediate step in copy- 
ing a drawing, or drawing an object already made, 
or in any case where any change of design is not 
permissible. 

The process of constructing the drawing should 
be systematic. With the mental conception of the 
object clearly fixed, decide first what views are nec- 
essary and determine their arrangement. After 
these preliminaries, the first step is to draw the main 
center lines or the lines of the principal mass of the 



object. This should be done in all the views to be 
made and the progress of the drawing should balance 
in all the views. The details should next be added 
systematically, putting in all the items of a series at 
one time, and the opposite sides of a symmetrical part 
in order. Center lines should be drawn before the 
lines of which they a .'e the center. Complete all thede- 
tails. Then draw witness and dimension lines and put 
in the dimensions. Add finish marks and notes. Fi- 
nally check all parts to see that the drawing is com- 
plete and correct. 

A sketch which is only a memorandum of design 
usually omits the minor details. These must be sup- 
plied by the draftsman according to his own judg- 
ment. The draftsman is also called upon to draw up 
minor details to meet certain specifications, and in 
this he must also follow his judgmeut or the custom 
of the blace, subject to the approval of the designer 
of the machine. 1 7-a. 1 7-b. 1 7-c. 1 7-b. 1 7-e. 
18. A working sketch is materially different from a 
memorandum sketch. It is in fact a working 
drawing made free hand, and hence is lacking in the 
mechanical accuracy of a drawing. Nevertheless, it 
must be as complete and as correct as a working draw- 
ing. There are three important uses for complete tech- 
nical sketches, the valuable feature in each case being 
the saving of time effected. A sketch can be made 
in much less time than a drawing and in these cases 
is indispensable. One purpose is for recording a 
design as it is worked out by the designer of a machine 
or a part, and this may be made with sufl^cient detail 
as to afford complete information to a draftsman who 
subsequently makes up a set of working drawings. 
Another purpose is tq serve as a shop drawing in emer- 
gency where the information must be supplied on short 

28 



notice, or when facilities for making a drawing are 
lacking. The third important purpose is as an inter- 
mediate step in producing drawings of a machine or 
detail already made. In making a sketch of an exist- 
ing object, follow a definite procedure. Study the 
object and decide what views are necessary, remem- 
bering that a free use of notes may save a consid- 
erable amount of drawing. On the other hand, it 
is not necessary to restrict the number of views to 
the number that will be used in the finished drawing. 
Start with cantsr linas or with finished (machined) 
faces, and show the various outlines as they appear 
to the eye, approximately to scale but without meas- 
urement either of the object or the sketch. Carry 
this through until all parts of the object are shown 
or described. Next decide what dimensions are to 
be used and draw in the witness and dimension lines. 
Finally measure the object (with a two foot rule, not 
the drafting scale) in as many places as there are 
dimensions required and enter the figures on the 
sketch. Calipers and other shop tools may be used 
for taking the dimensions. 18-a. 

A surface that is to be machined is indicat- 19. 
ed by a conventional mark resembling the letter 
f crossing the line to be finished. Any special finish 
is denoted by a note such as GRIND. ROUGH TURN. etc. 

The way in which a hole is to be made is usually 
indicated by a note in connection with the dimension 
as, for example, CORE 2 in. DIAM. TAP 5-8 in. etc. 

A conventional drawing of frequent occurrence 
is that representing the threads of a screw. An ac- 
curate drawing is tedious in execution and of no value 
as a working drawing. There would be one set of 
curved li.ies to represent the top of the threads, an- 
other set to represent the bottom of the threads, and 



a series of diagonal lines for the faces of the threads. 
All this can be drawn according to the rules of projec- 
tion, but is of no value in a working drawing. Con- 
ventional drawings of screw threads are shown in 
Chart II. Note that the outline shows the rod or bar 
before the threads are cut; the top and bottom of the 
threads are shown by straight lines. Several methods 
for showing threads are in use, with corresponding 
methods for tapped holes. 




20, There are parts used in the construction of 
machines which are stock pieces, bought ready 
made, instead of being made by the factory using 
them. There are also other parts of frequent and 
general use which are made in quantities according 
to standard specifications. It is not necessary to make 



drawings of these parts, as they are ordered by num- 
ber or size or trade name. It is necessary for the 
draftsman to know the sizes and specifications of 
these parts in order to make proper provision for 
their use in connection with the parts for which draw- 
ings are made. A large proportion of them are pieces 
used to fasten other parts together, such as screws, 
nuts, keys, and pins; also pipe and pipe fittings. 

There are two kinds of screw threads in use. 
The V thread has its sides inclined at an angle of 60° 
to each other and is perfectly sharp at both top and 
bottom. The U. S. Standard thread also has its sides 
at an angle of 60" to each other but has its top cut off 
to the extent of 1-8 of its pitch and the bottom filled 
in the same amount. 

A draftsman should have tables of various data 
convenient for reference. The following are among 
those most frequently used. U. S. Standard screw 
threads, including number of threads per inch for each , 
diameter of screw, and diameter at root of thread; 
dimensions of nuts and screw heads; dimensions of 
machine screws; wire and sheet metal gauges; di- 
mensions of keyways according to the standard of 
the place; dimensions of taper pins and cotters; di- 
mensions of standard pipe and pipe fittings; drill 
sizes for various kinds of tapped holes. 

Other tables for reference will save time in mak- 
ing calculations. A draftsman will accumulate a stock 
of such material pertaining especially to the line of 
work in which he is engaged. Trade catalogs are 
valuable sources of such information. 



REFERENCE TABLES. 



U. S. Standard Screw Threads. 

a, Diameter of body; b, Number of threads per inch; 
c, Area at root of thread. 
abcjabcabca b c 

1-4 20 .026 5-8 11 .202 1 1-4 7 .893 2 1-4 4 1-2 3.023 
5-16 18 .045 8-4 10 .302|l 3-8 6 1.057 2 1-2 4 3.719 
3-8 16.068 7-8 9.41911-2 6 1.295 2 3-4 4 4.620 



7-16 14 .093 
1-2 13 .126 



1 
11-8 



8.55] 13-4 5 1.746J 3 
7 .694 2 4 1-2 2.302 4 



3 1-2 5.428 
3 9.963 



Wrought Iron Pipe. 

b, Nominal size; e, Internal diameter; f, External 
diameter; g, Size of drill for i)ipe tap. 



d 


e 


f g 


1-8 


.27 


.40 11-32 


1-4 


.36 


.54 7-16 


3-8 


.49 


.68 37-64 


1-2 


.62 


.84 45-64 


3-4 


.82 


1.05 29-32 



d e f g i d 

1 1.05 1.32 1 9-64: 3 
1 1-4 1.38 1.66 11-2 14 

1 1-2 1.611.90123-32 5 

2 2.07 2.38 2 3-16i 6 

2 1-2 2.47 2.88 2 5-8 7 



3.07 
4.03 
5.05 
6.07 
7.02 



f 

3.50 
4.50 
5.56 
6.63 
7.63 



Machine Screws, h, G t'j.g3 number and num- 
ber of threads per inch; i, Diameter of body. 

Taper Pins, j, Gauge number; k, r>iameter 
of body at large end. Taper 1-4 in. diameter per foot. 



h 


i 1 h 


i 


h 


i 


J 


k 


j 


k j 


k 


2-56 


.08410-24 


.189 


18-18 


.295 ! 





.156 


4 


.250 8 


.942 


4-36 


.111112-24 


.216 


20-18 


.321 


1 


.172 


5 


.289 9 


.591 


6-32 


.137jl4-20 


.242 


24-16 


.374 


2 


.193 


6 


.341 10 


.706 


8-32 


.163!l6-20 


.268 30-14 


.452 


3 


.219 


7 


.409 





Weight of Materials. Per cubic inch. 

Cast iron. - .260 Cast brass, .284 to .304 

Wrought iron, - .278 Cast aluminum, - .093 

Steel, - - .283 Copper wire, - .321 

32 



MACHINE DRAWING-Job Sheet No. 8 



17-a. Make a series of drawings from notes and 
sketches supplied by the instructor. 

17-b. Make a complete working drawing of a collar 4 5-8 
in. diameter 'by 1 7-16 in. wide, with the hole 3 49-64 in. 
diameter. Finish all over. 

17-C. Make a complete working drawing of a coup>ling 
pin of which the body is 5-8 in. diameter by 3 1-4 in. 
long, and the head 1 in. diameter by 1-4 in. long. Drill 
1-8 in. hole through the -body 2 13-16 in. from the head. 
Chamfer outer corner of the head at 45° to leave 3-16 in. 
straight. 

17-d. Make a complete drawing of a flanged pipe of the 
following dim.ensions. Body is 6 1-8 in. outside diameter 
5 1-4 in. inside diameter, flanges 10 in. diameter by 1 
1-8 in. thick, fillets 3-8 in. radius, length 10 1-4 in. face 
to face. Finish both faces. Drill both flanges 8 holes 
7-8 in. drill on 8 1-2 in. bolt circle. 

17-e. Design and draw a bearing bracket to meet the 
following specifications. Make a preliminary sketch. 
The pad on which the foot of the bracket rests is 2 1-4 
in. by 5 in., machined, the fastening is to be two 1-2 in. 
cap screws ; the bracket is to carry a shaft 1 in. diameter 
which is parallel to the end of the pad, 1 1-2 in. out 
from the pad and 3 in. above it. 

i8-a. Make a series of sketches from a machine to be 
designated by the instructor. From the sketches make 
complete working drawings. 

—33— 



MACHINE DRAWING 

PART IV. - - TRACINGS AND BLUE PRINTS 

It is a general factory practice to furnish 21. 
blue prints of the drawings for use in the shops. 
Blue prints are made from tracings by a photographic 
process. The tracings are copies of the drawings 
made in ink on transparent cloth. The instruments 
used for this operation are the raling pen,<;omDasseg 
fitted with pen point, and bow pen, together with the 
tee square and triangles. For lettering and figures 
common writing pens are used. They should be of 
several sizes, rather stiff, and used with a finger 
stroke only. Black drawing ink is used and a pen- 
wiper is a necessary adjunct. 

The drawing to be traced is tacked to the drawing 
board after being carefully lined up with the tee 
square. The sheet of tracing cloth is spread over it, 
smooth side up, and held in place by thumb tacks. 
The cloth should be dusted with powered chalk, soap- 
stone or fuller's earth to make it take the ink. Rub 
the powder lightly over the surface with a soft cloth 
and remove all excess. 

The tracing is done by making ink lines on the 
cloth exactly covering the pencil lines of the drawing 
beneath. The thickness of the ink fines is gauged by 
the screw adjustme it of the ruling pens. This should 
be changed as few times as possible, drawing as many 
lines as convenient with each setting of the instra- 
ment. 21-2^. 21-b. 21-c. The work can be done 
with a saving of time by f ofiowing a systematic order. 
Trace first the center lines all over the drawing. 
These are light lines and it is essential that their in 



,ei:riections are at the exact points' on the drawing. 
Next trace the circles, and arcs, making as many as 
possible with each setting of the compasses. Be sure 
to set the point of the instrument on the exact inter- 
section of the center lines. Next trace the horizontal 
full lines, then the vertical and inclined lines. These 
are heavy lines. This completes the visible outlines. 
Next trace the broken lines representing the invisi- 
ble outlines. These are of mediam thickness, and the 
short dashes and spaces should be uniform. Next 
trace the hatching lines, if the drawing contains any 
sectional views, and the screw threads. The hatching 
lines are light lines and should be traced without any 
attempt to copy the lines as drawn on the paper. Make 
them uniform in thiskness and spacing so as to give 
the effect of a tint over the section surface. This com- 
pletes the drawing itself. Next trace the witness and 
dimension lines. These are light lines. It is not ne- 
cessary for them to be an exact copy of the drawing, 
but should be nearly so in the position of the lines and 
location of the figures. Next aid the figures and the 
notes as given. . Finally, check the entire tracing to 
see that nothing has been omitted. Construction lines 
used only for making the drawing are not to be 
traced. 21 -a. 

22. Certain lines of a drawing represent the edges 
of the object, or in other words the boundary 
lines between adjacent surfaces. To add to the clear- 
ness and effectiveness of a drawing, it is sometimes 
desirable to show a difference in the lighting of ad- 
jacent sur-faces of the object, by the use of shade lines 
in the drawing. The light is assumed to fall on the ob- 
ject from above, from the front and from the left, 
each at an angle of 45°. The degree of illumination 
on any surface depends upon its position and inclina- 



tion, and. every surface will be in one or the other 
of two groups, lighted and dark. Upper surfaces, 
front surfaces and left end surfaces are lighted; right 
hand and bottom surfaces are dark. To bring out 
this distinction in a drawing, a line separating two 
lighted surfaces is made the regular thickness, while 
a line separating a lighted surface from a dark one 
is made heavier. The use of shade lines is confined 
almost entirely to assembly drawings, where it helps 
to distinguish one piece from another. 

It is also of occasional value in detail drawings, to 
give an effect of relief not otherwise obtainable. In 
strictness, shade lines belong only to plane surfaces, 
but in practice, when used, they are applied to plane 
and curved surfaces indiscriminately, the simple rule 
being to make all lowerand right hand boundary lines 
heavy. Shade lines are never used on pencil draw- 
ings; only on inked-in drawings and tracings 

The making of blue prints is not a part of 23. 
the draftsman's business, but the process should 
be understood. As usually practised it is extremely 
simple. Prepared paper is used and the essential ap- 
paratus consists of a printing frame with a glass front 
and a tray for washing the prints. The operation is 
as follows. The tracing to be printed is placed in the 
frame with the inked side next to the glass; on this a 
sheet of the prepared paper is laid with the sensitized 
side next to the tracing. The back of the frame is ad- 
justed to hold the paper and tracing in close contact 
with each other against the glass. The frame is then 
exposed so that strong light will fall upon the tracing 
and through it upon the prepared paper. 

The ink lines of the tracing prevent the light 
from reaching the paper beneath them., After a 
suitable exposure, depending upon the strength of the 



lisht, the transparency of the tracing and the sensi- 
tiveness of the prepared papsr, the pa,:er is removed 
from the frame and thoroughly washed in clear wa- 
ter. The resu.t is a copy of the tracing showing 
white lines on a blue ground. The action of the 
light is such as to render the chemical preparation 
on the paper insoluble, while the parts which were 
covered by the ink lines of the tracing remain soluble 
and are washed out in the bath. The t.-acing is in no 
way affected by the process and may be used repeat- 
edly for making as many prints as may be requi.-ed. 



fl Never use a blotter on inked lines. 

^ Never leave the stopper out of the ink bottle. 

^ Never leave ink to dry in a ruling pen or compass 
pen. 

^ Never use the ruling pen free hand, that is, with- 
out a straight edge or curve to guide it. 

^ It is not the tracer's business to revise or in any 
way "edit" the drawing. The more nearly exact the 
tracing is to the drawing, the better the job. 



MACHINE DRAWING-Job Sheet No. 9 



2i-'a. Make a series of lines with the ruling pen on 
tracing ctoth, using the tee square and 'triangle so as to 
become used to the handling of the pen. Set the pen so 
that it will make a line as wide as the one designated 
"visible outline" on Chart I. This is a heavy line. A 
medium line is the width oif that designated "invisible" 
and "section plane." A light line is the width of the one 
designated "center line." Make several lines of each 
width. 

2i-b. Make the same kinds of lines as in 21-a, using 
the compasses fitted with ruling pen end, and using the 
bow pen. 

2I-C. Make a set of lines for reference as an Alphabet 
of lines. The set should comprise the following: 

1. Heavy solid line for visible outlines. 

2. Medium, broken line for invisible outlines. (The 
dashes should be 1-8 in. long with spaces 3-64in.) 

3. Medium, broken line for invisible outines of small 
extent. (Dashes 1-16 in. in. long, spaces 1-32 in. 

4. Light, broken line for center lines. (Dashes alter- 
nating 2 in. and 1-16 in., spaces all 1-16 in.) 

5. Light, broken line for witness and dimension lines. 
(Dashes 2 in., spaces 1-16 in.) 

6. Medium, broken line for location of sections. 
(Dashes alternating 1 in. and 1-16 in., spaces all 1-16 in. 

2i-d. Make tracings of such drawings as the instructor 
may designate. 



MACHINE DRAWING 

PARTY. PROJECTIONS 



A point is projected by passing a line 24. 
through it in any direction. The hne is a pro- 
jection line and any point on it is a projection of the 
given point. Let m be a projection of the point a 
and n of the point h; then a line joining the points 
m and u is a projection of a line joining the points 
a and h. In a similar way any line may be project- 
ed by projecting points in it, and an entire object by 
projecting all the lines composing its outlines. It is 
eviden; that an infinite number of projections can be 
made. To be of value they must be used according 
to some definite system. Several systems of projec- 
tion have been built up and are in use. 

If in [a given case all the projection lines are 
parallel the result is parallel projection. If in any 
given case the projections all he in one plane the 
result is plane projection. If in a given case the pro- 
jection lines are parallel and the projections all lie in 
one plane (parallel plane projection), and in addition 
the plane of projection is perpendicular to the pro- 
jection lines, the result i>-' orthographic projection. 
This is the system used in practically all working 
drawings. Working drawings are made in third 
angle projection 'which means that the plane of pro- 
jection is placed between the object and the point 
of view. Drawings are sometimes found, made in 
first angle projection, which results from putting the 
plane of projection beyond the object from the point 
of view. Isometric, cabinet and perspective projec- 
tion are other systems in use for special purposes. 



25. The arrangement of views in a working draw- 
ing is an application of third angle orthograph- 
ic projection. The plan or top view is made on a hor- 
izontal plane placed above the object, the points of 
which are projected upward by vertical projection 
lines. Front, side and eid views are obtained on ver- 
tical planes by m.ears of horizontal projection lines. 
The usual views in a working drawing correspond to 
the three standard planes of projection. These three 
planes are located at right angles to each other and 
are then folded or revolved into one plane which re- 
presents the plane of the drawing. This revolving 
of the planes of projection is equivalent to the un- 
folding of the box model used in Sec. 14 to demon- 
strate the correct arrangement of views. Of course 
the views are all drawn, actually, in one plane, but as 
they would appear if drawn on the respective projec- 
tion planes. 

26. The projection of a line which is parallel to the 
plane of projection is ecual in length to the line 

itself, but if the line is not parallel to the plane of pro- 
jection its projection is shorter than the line it^eli. 
This is the technical statement of the foreshortening 
in drawings which is a matter of common observa- 
tion. In a working drawing it is of no particular 
consequence, provided the line is shown in its proper 
length in some other view. If a certain part of an ob- 
ject cannot be shown in any of the regular views and 
it seems desirable to show the part without fore- 
shortening:, it is customary to draw it as it would ap- 
pear if p-ojested upon an auxilia-y plane of projection 
S9t up parallel to the given surface and then revolved 
into tha front visw plane. Such auxiliary views may 
be complete, or may shew only the detail which 
could not be clearly shown in the other views. 26-a. 



A drawing does not show surfaces, but on- 27. 
ly the boundaries or edges of the surfaces. It 
is evident that where one surface ends another begins, 
so that an edge belongs to two surfaces, being their 
intersection. The shape of the two surfaces which 
meet at an edge, and their relative position will de- 
termine the shape of the line which is their intersec- 
tion. 

A point is the beginning of all geometrical mat- 
ter. A moving point generates or marks out a line; 
a moving line generates a surface. A line by which 
a surface is generated may be either straight or 
curved and the generated surfaces will be of two cor- 
responding classes. Surfaces marked out by a mov- 
ing straight line are ruled surfaces, and include plane, 
single-curved and warped susfaces. A plane surfai'.e 
is one in which the generating straight line moves so 
as to always touch two directing lines which must be 
straight lines and either parallel or intersecting. A 
single-curved surface, such as the curved surface of 
of a cylinder or cone, can be made by rolling a plane 
surface. In such a surface, two adjacent elements, 
or positions of the generating line, are either parallel 
or intersecting, and consequently lie in one plane. In 
a warped surface the generating straight line moves 
so that adjacent elements are neither parallel nor in- 
tersecting. Hence, as two adjacent elements do not 
lie in a plane, a warped surface cannot be made by 
rolling or bending a plane surface. An example of a 
warped surface is the face of a screw thread. 

A surface marked out by a curved line moving 
along a curved path is a double-curved surface. The 
simplest form is the surface of a sphere. .Other exam- 
ples are the fillets and rounded corners of cylindrical 
pieces and numerous forms occurring in lathe work. 



28. Where two surfaces meet, there is a line belong- 
ing equally to both surfaces, and this intersec- 
tion follows the laws of both surfaces. The inter- 
section of two planes is always a straight line. The 
intersection of a plane and a cylindrical surface is 
either a straight line, a circle or an ellipse, depend- 
ing on the position of the plane relative to the axis of 
of the cylinder. The intersection of a plane and a 
conical surface is either a straight line, a circle, an 
ellipse, a parabola or a hyperbola, the so-called conic 
sections. Tha intsrsection of a plans and a spherical 
surface is always a circle. 

The drawing of a line may not show its true 
shape because the plane of projection may not be 
parallel to the plane in which the line may lie; and 
furthermore, some lines do not lie in a plane, as for 
example, the helix, which is a curve of three dimen- 
sions. The true shape of such a line cannot be shown 
on a plane, but is drawn by projecting it on two or 
more planes. 

The intersection of any two surfaces as seen from 
any point of view, (or as projected upon any plane of 
projection,) can be laid out by projecting points in 
the different views into the required view. Intersec- 
tions of many kinds are of constant occurrence in 
machine parts and must be represented in the draw- 
ings. A high degree of accuracy is seldom required. 
The intersection of two cylindrical surfaces is a typi- 
cal example, and the method of plotting this curve is 
shown in Chart III. Fig. 1 is a picture drawing rep- 
resenting a cylinder with a vertical axis intersecting 
a cylindrical surface having a horizontal axis. Fig. 
2 is a top view and Fig. 3 an end view of this piece. 
Fig. 4 is a front view, partially drawn, in which the 
intersection of the two surfaces is to be shown. It is 



obtained by locating on the top and end views a ser- 
ies of points of the intersecting line, and projecting 
them to the front view. A round dot in Fig. 1 indi- 
cates a point of the intersecting line, the same point 
being represented by A in the end view. Draw a ver- 
tical line through A and with the dividers transfer 




Plotting an In;:ersection. 

the dimension M to the top view at N. Draw a hor- ' 
izontal line to the left, cutting tne circle at B, which 
represents in this view the same point as A in the end 
view. Project A to the left and B downward until 
they intersect, at C, locating the same point in this 
view. Repeat this process for as many points as may 
be needed and then draw a smooth line through them. 
This is the required line, representing in this view 
the intersection of the surfaces. 28-a. 28-b. 28-c. 












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